where the experimental value \(a_\mu ^{\rm Exp} = (116\,592\,061\pm 41)\times 10^{-11} \)  is obtained by combining the earlier Brookhaven [1]} and the latest Fermilab Muon \(g-2\)  [2]} data, while the SM prediction is given by \(a^{\rm SM}_\mu = (116\,591\,810\pm 43)\times 10^{-11}\)  based on the state-of-art evaluations of various contributions [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]} (see e.g. Ref. [23]} for a recent review and references therein). In light of these precise measurements and calculations, this muon \(g-2\)  anomaly is usually regarded as an indication to the new physics beyond the SM. In the literature, there have already been many new physics attempts to resolve this anomaly (see e.g., Ref. [24]} for a recent review and references therein). It is worth to mention that, in the HUFT, the 3-form field \(\Omega \) , as a part of the spin gauge field, couples to the SM fermionic fields inevitably. Hence, it is highly probable to generate an extra contribution to the muon \(g-2\)  via its interaction with muons. Here we would like to carefully examine if the one-loop contributions induced by \(\Omega \)  could help us to ameliorate or even eliminate the \((g-2)_\mu \)  discrepancy. Furthermore, the scenario we are considering needs a relatively light \(\Omega \)  and a moderately large coupling to muons, which might potentially lead to the breakdown of perturbativity and unitarity. For that reason, we shall also take into account theoretical constraints from these issues in the framework of effective field theory.
